Disclosed is an authentication mechanism that provides much of the security of heavyweight authentication mechanisms, but with lower administrative and communicative overhead while at the same time not being limited to a 64-bit limit on the length of a cryptographic hash value. Removal of this limitation is achieved by increasing the cost of both address generation and brute-force attacks by the same parameterized factor while keeping the cost of address use and verification constant. The address owner computes two hash values using its public key and other parameters. The first hash value is used by the owner to derive its network address. The purpose of the second hash is to artificially increase that computational complexity of generating new addresses and, consequently, the cost of brute-force attacks. As another measure against brute-force attacks, the routing prefix (i.e., the non-node selectable portion) of the address is included in the first hash input.